For many applications it is of great importance to precisely determine the transition frequency between two energy states in an atom (or other quantum absorber such as a molecule, or an ion). An atomic frequency standard uses this transition frequency to define its output frequency while a magnetometer uses this transition frequency to measure the magnetic field strength. Because the environment, which the quantum absorber is exposed to, can perturb the energies of these two energy states, the corresponding transition frequency can also be perturbed. The choice of the two energy states depends on the specific application. An atomic frequency standard chooses these two energy states so that the transition frequency is insensitive to the environmental parameters. A sensor (e.g., a magnetometer) chooses these two energy states so that the transition frequency is sensitive to the physical quantity (e.g., the magnetic field strength) that it measures but insensitive to all the other environmental parameters.
To simplify the following discussion, the example of an atomic frequency standard will be utilized. However, the discussion also applies to the sensor applications. In one class of atomic frequency standards, the two energy states belong to the manifold of the ground state of a suitable atomic species, e.g., Rb or Cs. The transition frequency, which defines the output frequency of the atomic frequency standard, between these two energy states is in the microwave frequency range. In the following discussion, these two energy states are called state A and state B. Also there is an additional energy state, state E, which belongs to the manifold of the excited states. Further, it is assumed that the energies of the energy states, Eα (α=A, B, or E) satisfy the relation EE>EB>EA. In addition, it will be assumed that the allowed transition between state E and state A (or state B) has a transition frequency in the optical range.
At room temperature, state A and state B are nearly equally populated while state E is nearly un-populated. In this case, if the atoms are irradiated with a microwave field, it is difficult to observe the induced transition between state A and state B. However, if the atoms are irradiated with an optical field at the appropriate frequency, the atom in one of the energy states, say state A, will absorb a photon and make a transition to state E. When the same atom decays from state E to the ground state, some of the decays are to states different from state A. Therefore this optical-pumping process depopulates state A and generates a population difference between state A and state B. Consequently, the absorption of the applied optical field and the fluorescence are reduced. The relaxation process, such as collisions, re-populates state A. The efficiency of the optical pumping process is maximized when the frequency of the optical field, νL, is equal to the frequency of the transition between state A and state E, ν0≡(EE−EA)/h, where h is the Planck constant. For a simplified three-state atomic system, a conventional dither-and-phase-sensitive-detection servo loop can be used to keep νL=ν0.
Now, if the atoms are also irradiated with a microwave field at the frequency in the vicinity of the transition frequency between state A and state B, the induced transition will increase the population in state A. Hence the absorption of the applied optical field and the fluorescence are increased. If the applied microwave frequency, νM, equals the transition frequency between state A and state B, νBA≡(EB−EA)/h, both the absorption of the applied optical field and the fluorescence are maximized. Again a dither-and-phase-sensitive-detection servo loop can be used to keep νM=VBA.
Unfortunately, the atom under study exhibits an AC Stark Shift (light shift). That is, the energy difference between states A and B depends on the intensity of the applied optical field. As a result, νBA is a function of the intensity of the applied optical field used to optically pump the atoms. To provide a standard of high precision, a light source with an extremely stable intensity is needed. The cost of providing such a source significantly increases the cost of such an optically pumped atomic frequency standard.